But it is supposed to be so! At least in physics or mathematics (and the "harder" sciences), if there are multiple descriptions, they better be completely equivalent in the answers they give, otherwise all but one of them are wrong. It is possible that different fundamentally equivalent frameworks might be more suited to different problems (eg: Newtonian mechanics -vs- Lagrangian mechanics)

"The" in this context is used as a general classifier for all the science and mathematics related to quantum information. It wouldn't make sense to use "A theory of..." unless you're speaking of a particular case that doesn't fall under the general classification.

Perhaps interesting: Shannon's original information theory article is titled 'A Mathematical Theory of Communication', and when later released in book form was renamed 'The Mathematical Theory of Communication', due to the generality of information theory.

No, not at all. I also don't like what the implies instead of a.